My prof in my digital logic design course neglected to explain the implication operation properly and I’m having a hard time understanding what to do in a question on my current assignment. All the references (friends and web) I’ve tried don’t give me a very good explanation with regards to this problem, so here goes…
The question is basically as follows:
a) Show if the implication operation x–>y defined in the table is commutative and associative.
x y x-->y 0 0 1 0 1 1 1 0 0 1 1 1
Finding the minterm expansion gives the function x’+y, which is obviously commutative given it is an OR function, and I suppose it’s associative as well since there are only two variables, although I’m unsure if there’s anything more to the explanation than just that.
b) Is the operation (x–>y)(y–>x) commutative?
Since (x’+y)(y+x’) = (x’+y) = (y+x’) I assume this operation is commutative.
Then again, I’m not entirely clear on what x–>y and y–>x are supposed to mean. I guess this is my main problem: I don’t understand the implication function.
Thanks very much to whoever can help!